The universal tropical Jacobian \(\widetilde{\mathcal {J}}^{trop}_{g,n}\)  over \(\operatorname{\bf {LSch}}\)  comes equipped with a forgetful-stabilization morphism to the stack \(\widetilde{\mathcal {M}}^{trop}_{g,n}\)  of tropical curves over \(\operatorname{\bf {LSch}}\) , as defined in [1]}:
\(\begin{aligned}\widetilde{\Phi }^{trop}:\widetilde{\mathcal {J}}^{trop}_{g,n}& \longrightarrow \widetilde{\mathcal {M}}^{trop}_{g,n}\\\big \lbrace (\Gamma _s/\overline{M}_{S,s},D_s)\big \rbrace _s & \longmapsto \big \lbrace \Gamma _s^{st}/\overline{M}_{S,s}\big \rbrace _s,\\\big \lbrace \pi _f: (\Gamma _s)\rightarrow (\Gamma _t)\big \rbrace _{f\colon t\rightsquigarrow s} & \longmapsto \big \lbrace \pi _f^{st}: (\Gamma _s)^{st}\rightarrow (\Gamma _t)^{st}\big \rbrace _{f\colon t\rightsquigarrow s}\end{aligned}\) 
